Survival analysis with quantile regression models

Quantile regression offers great flexibility in assessing covariate effects on event times, thereby attracting considerable interests in its applications in survival analysis. But currently available methods often require stringent assumptions or complex algorithms. In this article we develop a new quantile regression approach for survival data subject to conditionally independent censoring. The proposed martingale-based estimating equations naturally lead to a simple algorithm that involves minimizations only of L-1-type convex functions. We establish uniform consistency and weak convergence of the resultant estimators. We develop inferences accordingly, including hypothesis testing, second-stage inference, and model diagnostics. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies. An analysis of a recent dialysis study illustrates the practical utility of our proposals.